Distributed source coding (DSC) encodes correlated data from multiple sources that do not communicate with each other. By modeling a correlation between multiple sources in a decoder with channel codes, DSC shifts the computational complexity from an encoder to the decoder. Therefore, DSC is frequently used in applications with complexity-constrained and resource-constrained encoders, such as those used in simple sensors, satellite imagery, and multimedia encoding in battery-operated consumer devices such as mobile telephones and digital tablets. In DSC, the correlated sources are encoded separately but decoded jointly. As an advantage, separate encoding of the sources can be performed with low computational overhead and simpler circuitry.
DSC is based on a lossless Slepian-Wolf entropy bound, which guarantees that two isolated encoders can encode correlated data as efficiently as though the encoders are communicating with each other. For the special case of jointly Gaussian sources, Wyner-Ziv bounds on the rate-distortion performance of a distributed codec also ensure that there is no loss with respect to conditional encoding, i.e., the case where the encoders are communicating with each other. DSC has been applied to images, videos and biometric data.
The most common method of implementing DSC to encode a correlated image, in the presence of a correlated side information image at the decoder, involves the use of a low density parity check (LDPC) code. That method first extracts bitplanes from the input image, either directly from quantized pixels or indirectly from a quantization of the transformed version of the image. Typically used transforms include blockwise transforms, such as a two-dimensional discrete cosine transform (DCT), a two-dimensional discrete wavelet transform (DWT), a H.264/AVC (Advanced Video Coding) transform, etc. After obtaining the bitplanes, each bitplane is subjected to LDPC encoding, and produces syndrome bits. Typically, the number of syndrome bits is smaller than the number of bits in the encoded bitplane, thus resulting in data compression.
To perform the decoding, the method makes use of an image that is statistically correlated with the image that was encoded. That image is referred to as a side information image. Bitplanes are extracted from the side information image, either directly from quantized pixels in that image, or from a quantization of the transformed version of the image. The bitplanes provide an initial estimate of the bitplanes of the desired image that is to be recovered. The initial estimate is fed to the LDPC decoding procedure in the form of log-likelihood ratios (LLRs), where positive LLRs indicating a higher likelihood of a decoded bit value of 0 and negative LLRs indicating a higher likelihood of a decoded bit value of 1. The LDPC decoding procedure is performed separately for each bitplane.
To decode each bitplane, the decoder takes as input the syndrome bits received from the encoder corresponding to that bitplane, and the LLRs determined for each bit using the corresponding bitplane of the encoded side information image, as explained above. Then, the decoder performs belief propagation to output an estimate of the decoded bitplane. Finally, the bitplanes are combined to produce the quantized transform coefficients, and then the quantization and transforms are reversed to give the desired decoded image.
This technique is useful when the encoding is highly constrained and has requirements of low computation complexity, low circuit complexity, or low power consumption. Because syndrome encoding typically has a smaller complexity than conventional image encoding procedures, such as Joint Photographic Experts Group (JPEG), JPEG2000, H.264/AVC, High Efficiency Video Coding (HEVC), etc, encoding one or more images in this distributed manner is beneficial, compared to encoding all the images using a standard encoding procedure.
Decoders for these applications, e.g., sensor networks, satellite data compression, etc., can typically tolerate a higher complexity or power consumption than the encoder. An advantage is that, for the same low-complexity encoder, sophisticated decoders can be designed, which better exploit the statistical correlation between the source image and the side information image, thereby achieving a syndrome rate that approaches the ideal Wyner-Ziv coding bounds.